Strong extension axioms and Shelah's zero-one law for choiceless polynomial time

Andreas Blass, Yuri Gurevich
2003 Journal of Symbolic Logic (JSL)  
This paper developed from Shelah's proof of a zero-one law for the complexity class "choiceless polynomial time," defined by Shelah and the authors. We present a detailed proof of Shelah's result for graphs, and describe the extent of its generalizability to other sorts of structures. The extension axioms, which form the basis for earlier zero-one laws (for first-order logic, fixed-point logic, and finite-variable infinitary logic) are inadequate in the case of choiceless polynomial time; they
more » ... ust be replaced by what we call the strong extension axioms. We present an extensive discussion of these axioms and their role both in the zero-one law and in general.
doi:10.2178/jsl/1045861507 fatcat:vaizcgxcrbhyjoo7alnzdatniu